You can do this in the material editor by adding a Custom node with the output set to float1 and the following code:
return ResolvedView.StereoPassIndex;
It will output 0 for the left eye and 1 for the right eye, so you can switch off it to drive any effects per-eye.
To make an object visible in one eye only, set the material blend mode to Masked, and connect the custom node to the Opacity output. To switch which eye it is, put a OneMinus node in between.